Polytope of Type {4,6,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,8}*768d
if this polytope has a name.
Group : SmallGroup(768,1090071)
Rank : 4
Schlafli Type : {4,6,8}
Number of vertices, edges, etc : 4, 24, 48, 16
Order of s0s1s2s3 : 3
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
4-fold quotients : {4,6,4}*192e
8-fold quotients : {4,3,4}*96
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := ( 1,49)( 2,50)( 3,51)( 4,52)( 5,53)( 6,54)( 7,55)( 8,56)( 9,57)(10,58)
(11,59)(12,60)(13,61)(14,62)(15,63)(16,64)(17,33)(18,34)(19,35)(20,36)(21,37)
(22,38)(23,39)(24,40)(25,41)(26,42)(27,43)(28,44)(29,45)(30,46)(31,47)
(32,48);;
s1 := ( 3, 4)( 5, 6)( 9,14)(10,13)(11,15)(12,16)(19,20)(21,22)(25,30)(26,29)
(27,31)(28,32)(33,49)(34,50)(35,52)(36,51)(37,54)(38,53)(39,55)(40,56)(41,62)
(42,61)(43,63)(44,64)(45,58)(46,57)(47,59)(48,60);;
s2 := ( 2, 3)( 5,12)( 6,10)( 7,11)( 8, 9)(14,15)(17,33)(18,35)(19,34)(20,36)
(21,44)(22,42)(23,43)(24,41)(25,40)(26,38)(27,39)(28,37)(29,45)(30,47)(31,46)
(32,48)(50,51)(53,60)(54,58)(55,59)(56,57)(62,63);;
s3 := ( 1, 7)( 2, 8)( 3, 5)( 4, 6)( 9,13)(10,14)(11,15)(12,16)(17,23)(18,24)
(19,21)(20,22)(25,29)(26,30)(27,31)(28,32)(33,39)(34,40)(35,37)(36,38)(41,45)
(42,46)(43,47)(44,48)(49,55)(50,56)(51,53)(52,54)(57,61)(58,62)(59,63)
(60,64);;
poly := Group([s0,s1,s2,s3]);;

```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s0*s1, s1*s2*s3*s1*s2*s3*s1*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(64)!( 1,49)( 2,50)( 3,51)( 4,52)( 5,53)( 6,54)( 7,55)( 8,56)( 9,57)
(10,58)(11,59)(12,60)(13,61)(14,62)(15,63)(16,64)(17,33)(18,34)(19,35)(20,36)
(21,37)(22,38)(23,39)(24,40)(25,41)(26,42)(27,43)(28,44)(29,45)(30,46)(31,47)
(32,48);
s1 := Sym(64)!( 3, 4)( 5, 6)( 9,14)(10,13)(11,15)(12,16)(19,20)(21,22)(25,30)
(26,29)(27,31)(28,32)(33,49)(34,50)(35,52)(36,51)(37,54)(38,53)(39,55)(40,56)
(41,62)(42,61)(43,63)(44,64)(45,58)(46,57)(47,59)(48,60);
s2 := Sym(64)!( 2, 3)( 5,12)( 6,10)( 7,11)( 8, 9)(14,15)(17,33)(18,35)(19,34)
(20,36)(21,44)(22,42)(23,43)(24,41)(25,40)(26,38)(27,39)(28,37)(29,45)(30,47)
(31,46)(32,48)(50,51)(53,60)(54,58)(55,59)(56,57)(62,63);
s3 := Sym(64)!( 1, 7)( 2, 8)( 3, 5)( 4, 6)( 9,13)(10,14)(11,15)(12,16)(17,23)
(18,24)(19,21)(20,22)(25,29)(26,30)(27,31)(28,32)(33,39)(34,40)(35,37)(36,38)
(41,45)(42,46)(43,47)(44,48)(49,55)(50,56)(51,53)(52,54)(57,61)(58,62)(59,63)
(60,64);
poly := sub<Sym(64)|s0,s1,s2,s3>;

```
Finitely Presented Group Representation (Magma) :
```poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s0*s1,
s1*s2*s3*s1*s2*s3*s1*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

```
References : None.
to this polytope